An application of the rational sine-Gordon method to the Hirota equation

Abstract

In this study, the analytical solution of the Hirota equation by using the rational sine-Gordon expansion method (RSGEM) has been investigated. For this purpose, the mentioned model is converted into an ordinary differential equation by using a wave transformation. After the balancing procedure, a set of equation system is found. The solutions of the equation system give coefficients both in the considered solution form and in the model. The proposed technique gives new analytical solutions including the dark soliton solutions, bright soliton solutions and periodic wave solutions corresponding to the appropriate coefficient values. We also give geometric interpretations of the obtained solutions to understand the physical meaning better.